Question 30
I give Ann and Bill two consecutive positive integers (for instance Ann 7 and Bill 6). They know their numbers are consecutive, they know their own number, but they do not know the number I gave to the other one. Then I heard the following discussion: Ann said to Bill: “I don’t know your number”. Bill said to Ann: “I don’t know your number”. Then Ann said to Bill: “Now I know your number! It is a divisor of 20.” What is Ann’s number?